Interpretations of the Aharonov-Bohm effect

[Demystifier]

But the physical part of QT is very clear, because it describes, as far as we know today, correctly all observations. It predicts the probabilities for the outcomes of measurements given the state of the measured system.

Nobody denies that. But some people want to understand the non-physical part. Obviously, physics cannot answer all the questions that humans care about. Some physicists want a strict separation between physics and non-physics, and want to ban questions that combine insights from both sides. They are afraid that such combinations will ruin the purity of physics, and they certainly will. But too much purity is not a good thing, some mixture of physics with non-physics is welcome. Exactly how much of such a mixture is welcome, and how much is too much, there is no consensus on that.

 

[PeterDonis]

some people want to understand the non-physical part.

QT is a theory of physics. What "non-physical part" would such a theory have?

The issue that I see is that, at least for some, QT is an incomplete theory of physics. It allows you to predict probabilities for measurement results, but doesn't tell you "what is really going on" the way that classical theories did.

Obviously, physics cannot answer all the questions that humans care about.

This is not at all the same as claiming that a physical theory should have a "non-physical part".

In fact, it's not even the same as claiming that other things that humans care about are not ultimately dependent on physics. To most physicists, they are, since they are all ultimately made of the things that our theories of physics describe.

 

[Fra]

What is observer gauge?

The observer gauge I see it as a "thinking tool", and guiding principle for theory building to use your terminology.

It conceptually see it as corresponding to the choice of mathematical information structure that is associated with an observer, and which encodes the effective "hilbert space" for that observer, or whatever the generalization would be called. The corresponding "transformation" would generate all possible observers, and the gauges itself can be thought of as what gives distinguishes observers. What the explicit full emergent observer symmetry is like from the agent perspective that corresponds to our world is of course an open question, this is the million dollar question I guess.

But roughly speaking, this emergent symmetry would be expected to split off into a spacetime part and and internal structure part. But the thinking tool has the ambition to explain, why 4D, and what the symmetry groups of particle physics are like they are. And why no other symmetries are seen.

Traditionally by "observer" and observer invariance we only mean the reference/coordinate frames. ie. special and general relativity. But once you adopt the agent stance, it seems quote obvious that there is much more descriptors to an observer than it's motion in spacetime. It also has it’s internal degrees of freedom, and some mass or complexity limit with has the effect of a lossy retention of the full interaction history.

The difference in the thinking tool, is that the "freedom to choose" observer is not void of physical siginficance. Instead of thinking of it as a mathematical choice that makes not difference. Difference observers here - while all equally valid - have different fitness. And the set of observers is considered the real population in the real universe, not just a fictive ensemble.

/Fredrik

 

[Davephaelon]

An interesting paper i found today that might be relevant: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.040101
(https://arxiv.org/abs/1110.6169)

and a reply to the above paper: https://arxiv.org/abs/1604.05748

This paper by Lev Vaidman I find very interesting. I'm only able to read the abstract for now, but what he seems to be saying, is that the Aharonov-Bohm (AB) effect is essentially the same thing as quantum entanglement, and there's no need to invoke the potential concept to explain the AB effect. This is appealing as it brings the AB effect under a common roof with other phenomena that are explained by entanglement yielding a simplification; sort of like when Maxwell united electricity and magnetism. I'll print out the paper at our local library tomorrow, though I suspect it will be quite technical and over my head.

 

[Davephaelon]

I should have read the rebuttal to Vaidman's paper, by Aharonov, Cohen, and Rohrlich, that is also linked above before making the above comment. It's actually not too hard to follow their analysis at the beginning, but I will have to do some deep thinking to follow their arguments all the way through to the end of the short paper.

 

[Demystifier]

What "non-physical part" would such a theory have?

I was using the terminology of @vanhees71, for whom "non-physical" part means interpretational aspects that do not affect measurable predictions. Each physical theory, in that sense, has a "non-physical" interpretational part. For example, in Newtonian celestial mechanics it is taken for granted that the planet Mars is there even when nobody observes it. Of course, if I was not replying to vanhees71, I would not call it "non-physical".

 

[Demystifier]

This is appealing as it brings ... under a common roof with other phenomena that are explained by entanglement yielding a simplification

Then you might be interested in my https://arxiv.org/abs/1203.1139

 

[vanhees71]

QT is a theory of physics. What "non-physical part" would such a theory have?

The issue that I see is that, at least for some, QT is an incomplete theory of physics. It allows you to predict probabilities for measurement results, but doesn't tell you "what is really going on" the way that classical theories did.

According to QT the probabilities are all there is, i.e., the observables only take determined values if the system is prepared in a corresponding state (in the most simple case described by an eigenstate of the self-adjoint operator presenting this observable). All other observables do not take determined values before measured. This were only incomplete a description if you could empirically demonstrate that this prediction of "indeterminacy" is wrong, but there are very strong hints that in fact QT is correct. All Bell text demonstrate at least that there is no local HV model that all observables take predetermined (but maybe unknown) values all the time. So people, who claim that QT were incomplete, should have some empirical evidence for it. Philosophical prejudices are not argument within the natural sciences!

This is not at all the same as claiming that a physical theory should have a "non-physical part".

In fact, it's not even the same as claiming that other things that humans care about are not ultimately dependent on physics. To most physicists, they are, since they are all ultimately made of the things that our theories of physics describe.

What should such a "non-physical part" be?

There is of course much more humans care about than the natural sciences investigate and describe, but of course the human condition as a whole depends on the objective natural laws described by the natural sciences.

 

[martinbn]

I was using the terminology of @vanhees71, for whom "non-physical" part means interpretational aspects that do not affect measurable predictions. Each physical theory, in that sense, has a "non-physical" interpretational part. For example, in Newtonian celestial mechanics it is taken for granted that the planet Mars is there even when nobody observes it. Of course, if I was not replying to vanhees71, I would not call it "non-physical".

This is not a good example. In Newtonian mechanics "Mars is there" is not an interpretation but part of the core theory. The observalbes, in this case position, have values at all times whether they are being measured or not.

 

[JandeWandelaar]

Is there any reason to switch the name to BA from AB?

QT is a theory of physics. What "non-physical part" would such a theory have?

The issue that I see is that, at least for some, QT is an incomplete theory of physics. It allows you to predict probabilities for measurement results, but doesn't tell you "what is really going on" the way that classical theories did.This is not at all the same as claiming that a physical theory should have a "non-physical part".

In fact, it's not even the same as claiming that other things that humans care about are not ultimately dependent on physics. To most physicists, they are, since they are all ultimately made of the things that our theories of physics describe.

Physical theories can't describe though what a particle is. You can say it's an excitation of a field, an operator valu8ed distribution, but they create or destroy states which refer to wavefunctions. A wavefunction gives the probabilities of finding particles, A particle is said to be a point-like 1D "structure". Or maybe a string or even something more exotic. But then again, what stuff is a string, or why does it vibrate? What is space made of? The content seems non-physical, and maybe lies at the root of consciousness.

 

[JandeWandelaar]

Could it be that the AB effect is a physical realization of the gauge transformation used to infer the A-field in QED? So, the other way round?

 

[vanhees71]

No! The AB effect is an observable effect and thus gauge invariant. A gauge transformation is a change between different description of the same physical realization. It's not anything that's realized in nature (however you think that nature realizes mathematical operations of our theories describing her).

 

[JandeWandelaar]

No! The AB effect is an observable effect and thus gauge invariant. A gauge transformation is a change between different description of the same physical realization. It's not anything that's realized in nature (however you think that nature realizes mathematical operations of our theories describing her).

But the phase of the projected interference pattern has shifted globally. So can't we say a global phase shift of the electron field will cause the A-field as generated in the experiment? If we locally gauge the electron field, the A-field comes into being (charge being the generator of the gauge).

 

[vanhees71]

The phase is gauge invariant, it's given by the magnetic flux through the solenoid. The physical situation is the presence of this magnetic flux. The potential is used to describe it in the formalism of QT, based on the Hamiltonian description. The observed shift of the interference pattern is the same for any gauge, i.e., it cannot be used to determine a potential in any specific gauge.

 

[Fra]

A gauge transformation is a change between different description of the same physical realization. It's not anything that's realized in nature

What if two real observers can be argued to have their optimal fixed gauge choices, then this transformation should have a physical manifestation in the relations (interactions) between two physical agent-subsystems?

One usually thinks the math is just a dressing but if the information encoded in the math needs to be physically encoded, then occams razor may get a new meaning of the beauty of simplicity as simplicity may be economical to the agent? Ie relational economy.

/Fredrik

 

[vanhees71]

A gauge transformation just changes between two different descriptions of the same physical situation. There is no way to physically make any specific gauge "preferred". This has nothing to do with observers or agents or other metaphysical ideas.

 

[JandeWandelaar]

The phase is gauge invariant, it's given by the magnetic flux through the solenoid. The physical situation is the presence of this magnetic flux. The potential is used to describe it in the formalism of QT, based on the Hamiltonian description. The observed shift of the interference pattern is the same for any gauge, i.e., it cannot be used to determine a potential in any specific gauge.

But can't we infer the presence of the A-field by observing the phase shifts globally over the screen (the pattern moving to the left or right)?

 

[Fra]

A gauge transformation just changes between two different descriptions of the same physical situation.

But if we add the requirement that a real description as opposed to a fictious one needs to physically encoded in the agent part. Then one expects as isomorphism between mathematics and ontic part of the agent.

I am well aware that this is not the standard reasoning of course. But i am trying to provoce another perapective in the discussion as a thinking tool.

/Fredrik

 

[JandeWandelaar]

The phase is gauge invariant, it's given by the magnetic flux through the solenoid. The physical situation is the presence of this magnetic flux. The potential is used to describe it in the formalism of QT, based on the Hamiltonian description. The observed shift of the interference pattern is the same for any gauge, i.e., it cannot be used to determine a potential in any specific gauge.

If we change the phase globally, then no difference will be seen. But don't we change the phase here partially globally, so to speak?

 

[vanhees71]

But can't we infer the presence of the A-field by observing the phase shifts globally over the screen (the pattern moving to the left or right)?

The A-field is unobservable. You cannot in any way observe its presence. Once more: The AB effect is gauge-independent, as it must be for an observable effect!

 

[JandeWandelaar]

The A-field is unobservable. You cannot in any way observe its presence. Once more: The AB effect is gauge-independent, as it must be for an observable effect!

But the phase change of the pattern is visible. The change indicates something has changed between emitter and screen.

 

[vanhees71]

Yes, the change is the absence/presence of a magnetic field.

 

[JandeWandelaar]

Yes, the change is the absence/presence of a magnetic field.

But the magnetic field is zero before and after. There is only an A-field (or not). Which is exactly the reason for assigning it reality.

 

[Lord Jestocost]

... Each physical theory, in that sense, has a "non-physical" interpretational part ...

Indeed, each physical theory comprises more than its 'physical part', when 'physical part' merely means its 'syntactics'. Hans Primas in “Chemistry, Quantum Mechanics and Reductionism, Perspectives in Theoretical Chemistry”:

“According to Morris (1938), the three dimensions of semiotic analysis are the semantic, the syntactic and the pragmatic dimension. Semantics deals with relations of signs to their objects, syntactics deals with the formal relations of signs to one another, and pragmatics deals with the relations of signs to their interpreters.

We consider a scientific theory to be a semiotic system consisting of the following three parts:

(i) syntactics, realized as a mathematical formalism dealing with the logico-mathematical structure of the theory;

(ii) semantics, realized by an interpretation that deals with the relation of the mathematical symbols to the objects which they denote;

(iii) pragmatics, consisting of regulative principles of a normative kind, describing the relation of the theoretical terms to their interpreters and the possible contexts of use.”

 

[vanhees71]

But the magnetic field is zero before and after. There is only an A-field (or not). Which is exactly the reason for assigning it reality.

No it is not. If you don't change anything physical than the interference pattern won't change too. Check it: If you make $\vec{A}=-\vec{\nabla} \chi$ everywhere, there's no shift of the interference pattern compared to $\vec{A}=0$, as it must be, because in this case, of course, $\vec{\nabla} \times \vec{A}=\vec{B}=0$ and thus also $\Phi=0$.

For what I refer to as the Aharonov-Bohm effect, see

https://en.wikipedia.org/wiki/Aharonov–Bohm_effect#Magnetic_solenoid_effect

In the ideal case of an infinite solenoid you have $\vec{B}=\text{const}$ inside but $\vec{B}=0$ outside the solenoid. To derive $\vec{A}$ let's calculate in the Coulomb gauge, where $\vec{\nabla} \cdot \vec{A}=0$. Then (for magnetostatics) you have
$$-\Delta \vec{A}=\vec{j}.$$
For the solenoid we can set (with $N/L$ windings per unit length)
$$\vec{j}=\frac{I N}{L} \delta(R-a) \vec{e}_{\varphi}=\frac{I N}{L a} \vec{e}_z \times \vec{r} \delta(R-a)$$
in standard cylinder coordiantes $(R,\varphi,z)$. With the ansatz
$$\vec{A}=f(R) \vec{e}_3 \times \vec{r}$$
you get after some algebra from the jump condition for $f'$ due to the $\delta$ distribution and the continuity of $f$ at $R=a$
$$f(R)=\begin{cases} \frac{I N a^2}{2 L R^2} & \text{for} \quad R>a, \\
\frac{I N a}{2L} & \text{for} \quad R<a. \end{cases}.$$
This gives indeed the well-known result
$$\vec{B}=\vec{\nabla} \times \vec{B} = \begin{cases} 0 & \text{for} \quad R<a, \\ I N/L & \text{for} \quad R<a. \end{cases}$$
The phase of the electron wave function relevant for the AB effect is the line integral of $A$ along an arbitrary path around the solenoid. The phase is independent of this path and can thus be calculated using an arbitrary circle parallel to the solenoid. According to Stokes's Law the result is the total flux of the magnetic field through the solenoid,
$$\Phi=\pi a^2 B=\pi a^2 N I/L.$$
This is a gauge-invariant result.

 

[Demystifier]

This is not a good example. In Newtonian mechanics "Mars is there" is not an interpretation but part of the core theory. The observalbes, in this case position, have values at all times whether they are being measured or not.

By that logic, one could say that "particle is there" is not a Bohmian interpretation but part of the core Bohmian theory. And yet, for some reason, people say that Bohmian mechanics is an interpretation of QM, not a theory on its own. How do you define the difference between interpretation and theory?

 

[martinbn]

By that logic,

What is wrong with the logic? Do you disagree with what I said?

By that logic, one could say that "particle is there" is not a Bohmian interpretation but part of the core Bohmian theory. And yet, for some reason, people say that Bohmian mechanics is an interpretation of QM, not a theory on its own. How do you define the difference between interpretation and theory?

That is a question for those people. I think that BM is a different theory.

 

[PeterDonis]

the magnetic field is zero before and after.

Not everywhere. If you have a region of space where there is no magnetic field anywhere (for example, a double slit experiment with no solenoid placed between the slits), there will be no Aharonov-Bohm effect.

 

[PeterDonis]

What should such a "non-physical part" be?

According to @Demystifier, it's what you said it was:

I was using the terminology of @vanhees71, for whom "non-physical" part means interpretational aspects that do not affect measurable predictions.

 

[PeterDonis]

Physical theories can't describe though what a particle is.

Depends on the theory. QM doesn't, but classical physics did. That's why some people think QM is an incomplete theory.

 

[vanhees71]

But QM precisely describes "what a particle" (at least there's no known counterexample).

 

[PeterDonis]

QM precisely describes "what a particle"

It does? I thought you said it only describes probabilities:

According to QT the probabilities are all there is

 

[vanhees71]

Yes, that's no contradiction, because all there is concerning particles are probabilities for the outcome of measurements of observables related to the particles. That's a "complete description", as far as we know, because there is no hint for "hidden variables" allowing for a deterministic description. All empirical evidence rules out only local hidden-variable theories.

 

[PeterDonis]

all there is concerning particles are probabilities for the outcome of measurements of observables related to the particles.

I understand that that is your opinion. Not everyone shares it. That's why some people consider QM to be incomplete.

 

[vanhees71]

Fine, but it should be clear that all physical theories are complete as long as there is no reproducible phenomenon that proves them wrong. Then you need to refine the theory or even find a completely new one. The old theory then doesn't become completely obsolete but you learn about the constraints of their applicability. There's no constraint yet known concerning quantum theory.

It's also clear that there's still no satisfactory quantum theory of the gravitational interaction. In this sense QT is also incomplete, but as far as particle physics is concerned, quantum gravity effects are very hard to observe, so that at least FAPP concerning particles QT is complete.